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Evaluate the following integrals and choose the correct option: integral (1)/(sqrt(1-x2)) dx integral (1)/(1+x2) dx

Mathematics

ScanSolve AI Answer

Answer

C\text{C}

Step-by-step solution

2 steps
  1. Solve Question 1.

    The integral ∫11−x2dx\int \frac{1}{\sqrt{1-x^2}} dx is a standard integral.

    ∫11−x2dx=sin⁡−1x+C\int \frac{1}{\sqrt{1-x^2}} dx = \sin^{-1}x + C

    Comparing this with the given options, option C matches.

    The final answer is C\boxed{\text{C}}

  2. Solve Question 2.

    The integral ∫11+x2dx\int \frac{1}{1+x^2} dx is a standard integral.

    ∫11+x2dx=tan⁡−1x+C\int \frac{1}{1+x^2} dx = \tan^{-1}x + C
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